That would be a nice feature to auto-detect the value for --strip option. I never used -p as a feature, rather as an nuisive need to know the correct -p value. To implement this it is enough to know the lowest strip level when the directory or patched file exists. There is no need to do deep search as the simple guess works in 99% of the cases. In case auto-strip fails patch should fallback to the default behavior.
-- @midenok